Q & A: stability of hydrogen vs. positronium

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Why is a Positronium not stable like a hydrogen atom? If uncertainty principle explains why electron does not fall into hydrogen nucleus (proton), how come the same mechanism does not prevent the electron from falling into (colliding with) positron in Positronium?- Anonymous

A:

Actually, the uncertainty relations only account for why there's little electron wave function at the proton, not zero. So if the hydrogen atom could get to a lower energy state by electron-proton combination, it ultimately would. It happens that neutrons have slightly higher rest energy than the electron-proton combination (we'll ignore the neutrino) so the process doesn't happen without special unlikely energy input.

On the other hand, an electron and positron (anti-electron) can combine leaving only two photons, with no rest energy. When that happens, it's irreversible for all practical purposes.

Mike W.

(published on 10/16/2011)

Follow-Up #1: sub-atomic particle combinations

Q:

That makes sense. but what is "the mechanism" that permits (makes likely?) that (1) an electron + a positron -(much greater probability or almost unidirectional phenomenon)->>> two photons? and (2) a neutron (higher mass)->a proton + an electron (an hydrogen atom, lower energy than an isolated neutron)?
Case (2) looks like charge (proton and electron charge) is still retained (somehow separated?) inside neutron (is this correct?) and maybe electron and 3 quarks are somehow mixed inside a neutron? but I am not sure what they are doing inside a neutron and their states etc. and somehow an electron feels repulsion (because less probability or unstable? ->yeah but why?) inside a neutron and jumps out to form an orbital and the system forms an hydrogen. Still not completely clear why this must be that way. (maybe what I am asking here is similar to why "Pauli exclusion principle" must be that way. or similar to why you need energy to climb up a mountain or against potential gradient. and what is happening to the structure of a (potential) field in reality or in very very small scale?). Field theory can explain many things but does field exist in reality? or something else is in nature and under particular case it behaves like field?
Case (1) looks very mysterious in the sense that I cannot imagine much at the conversion event that it looks like a magic (particles with seemingly very different properties pop out (electron/positron vs two photons) after the event.). And the charges are not separated (seemingly disappear?)? What is happening at or near the particles conversion event? You say "wave function" predicts the behaviors of electron (and other massive? particles?) but what about "massless" particles? If "wave function" is not applicable to massless particles like photons, maybe it cannot describe the massive-massless particles conversion event like positron-electron->photons? Is this correct or wrong? and why?- Anonymous

A:

That's a lot of questions, so I'll probably miss some aspects of what you're asking.

I'm not sure what you mean by "mechanism" but in general there's nothing that feels like a familiar mechanism in these quantum processes.

There's no electron inside a neutron- it's really gone. To squeeze an electron into that volume would require it to have enormous kinetic energy. Its conserved quantities, most noticeably charge, remain of course.

Massless particles (photons and gluons) have wavefunctions, just like massive ones.

As to whether quantum fields "exist in reality", that's a philosophical question whose answer is somewhat subjective. So far as we can tell, nothing exists in nature except quantum fields.

The apparent unidirectionality of the e+p -> 2 photons reaction is not intrinsic to the process itself, but just reflects the types of non-equilibrium collisions that we can easily make. At an earlier hotter time, when the equilibrium state had lot's of e's and p's, the process routinely went both ways.